The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1 3X+2  1  1 3X  1  1  2  1 2X  1  1 2X+2  1  1 3X+2  1  1  1 3X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0 X+2  X  2  0 3X+2  2 3X  1  1  1  1  1  1  1  1  1  1
 0  1 X+1 3X+2 2X+3  1 X+3  2  1 3X 2X+1  1  0 X+1  1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 X+1  1 3X+2 2X+3  1 3X X+3  1 2X+1  2  1 2X  1 X+1 3X+2  1 X+3 2X+3  1 2X+2 3X 2X+1  1 X+2  0  X  2  0 3X+2  2 3X  0 3X+2  2 3X 2X X+2 2X+2  X  1  1  1  1  1  1  1  1 3X+1 3X+3  3  1 X+1 2X+3 3X+1 X+1 2X+1 3X+1
 0  0 2X  0  0  0  0 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X  0  0 2X  0 2X 2X 2X 2X  0  0 2X  0  0 2X 2X  0  0  0 2X 2X  0 2X 2X 2X  0  0 2X 2X  0  0 2X 2X 2X  0 2X  0  0 2X 2X 2X
 0  0  0 2X  0 2X 2X 2X 2X  0 2X  0  0  0 2X  0  0 2X 2X 2X  0 2X 2X  0 2X  0  0  0 2X 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0 2X 2X  0 2X  0 2X  0  0 2X 2X  0  0 2X  0 2X 2X  0 2X  0  0 2X  0 2X  0  0 2X 2X 2X 2X 2X 2X  0 2X
 0  0  0  0 2X  0 2X 2X 2X 2X  0 2X 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0  0  0 2X  0  0 2X 2X  0 2X  0 2X 2X  0 2X  0 2X  0  0  0  0  0 2X 2X 2X  0 2X 2X  0 2X 2X  0  0  0 2X 2X 2X

generates a code of length 82 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+264x^78+64x^79+270x^80+64x^81+720x^82+64x^83+270x^84+64x^85+264x^86+1x^100+1x^112+1x^116

The gray image is a code over GF(2) with n=656, k=11 and d=312.
This code was found by Heurico 1.16 in 0.422 seconds.